The present invention concerns a perfect geodesic lens for waveguides, and in particular for electromagnetic and surface acoustic waves, particularly suitable to be inserted in optical integrated circuits. (P. K. Tien: Integrated optics and new wave phenomena in optical waveguides. Reviews of Modern Physics, vol. 49, pages 361-420, April 1977).
The lens to which the present invention refers, pertains to the class of geodesic lenses and is formed by a substrate having a convenient non plane surface, but a convex or a concave one, on which the waveguide lies. (G. C. Righini, V. Russo, S. Sottini, G. Toraldo di Francia: Geodesic lenses for guided optical waves, Applied Optics, vol. 12, pages 1477-1481, July 1973). In the case of optical integrated circuits the waveguide is represented by a thin film of a generally dielectric material having a refraction index higher than that of the material forming the substrate. The substrate is generally a semi-conductor manufactured in glass or in special crystals through techniques peculiar to the optical field.
Geodesic lenses operate only according to curvature of the waveguide; the propagation in the thin film takes place according to the geodetics of the thus obtained bidimensional Rieman space. Any discontinuity in the guide, (as it occurs in the case of other types of lenses, due to variations in the thickness or the refraction index), is avoided.
The simplest geodesic lens is a portion of a spherical surface (a quarter of a spherical surface behaves as a perfect lens) but it shows a discontinuity at the input and at the output of the lens, which causes losses in the guide. It is well known that the aberrations of a portion of a spherical lens may be corrected by coupling the lens to a second lens of a different type (cf. for instance U.S. Pat. No. 3,917,384: High resolution lenses for optical waveguides). Problems of modal conversion, however, arise and the production complexities increase.
In the field of purely geodesic lenses, to obtain perfect and correct lenses, use has to be made of aspherical surfaces, of the revolution type, in order to avoid serious fabrication difficulties.
Still the problem connected with the discontinuities, or conflection lines, at the input and at the output, remains unsolved. The addition to the lenses of a toroidal junction, which would not affect substantially the properties of the lenses, has been considered. A better solution, however, to this problem is to foresee the continuity of the surface of the lens already in its design. This aim can be attained by applying the equivalence principle between lenses presenting a distribution of the refraction index (generalized lenses of Luneberg) and geodesic lenses. Following this principle a geodesic lens was actually obtained, the profile of which was the result of a numerical calculation: by approximation the lens was thus divided into a high number of rings (D. Kassai et al.: Aberration corrected geodesic lens for integrated optics circuits, Digest of technical papers, Topical Meeting on Integrated and Guided Wave Optics, Salt Lake City, Jan. 16-18, 1978).
A direct method is also known which brings an exact solution for the profile of geodesic lenses, perfect and without discontinuities, where the equivalence principle is not followed.
This method, which at an earlier stage was proposed for applications in the field of microwaves (G. Toraldo di Francia, Un problema sulle geodetiche delle superfici di rotazione che si presenta nella tecnica delle microode, Atti della Fondazione Ronchi, XII year, pages 151-172, 1957), has been adopted by the inventors of the present invention to manufacture geodesic lenses for integrated optical circuits.
The lenses which may be obtained according to this method are formed by two parts, linked up with continuity to each other. The inner one, which constitutes the actual lens, is contained within a parallel B of radius b, whereas the outer one, delimited by a parallel A of radius a, acts as a junction to the external plane surface of the lens. A guided collimated beam, having a maximum aperture equal to the diameter 2b, is perfectly focused, whereas the rays which do not cross B are not focused. Such type of lenses presents the drawback that its focus lies on a point parallel A, i.e. exactly at the limit between the plane surface and the concave or convex area of the lens.
The object of the present invention is to realize geodesic lenses, which not only are free from said limitations, i.e. can perfectly focus a collimated beam at any predetermined point in the plane external to the lens depression, but, very importantly, they also are able to provide a perfect image (without aberrations) of a linear or point source placed at finite distance from the lens axis in the plane external to the lens itself.
Such an object, according to the invention, is obtained with a geodesic lens for waveguides characterized in that it is formed by four concentric zones, of which the two outer ones, having an external radius a and b, are portions of a plane surface, the central zone, having a radius d, represents the actual lens, and the remaining zone, having an external radius c, is a connecting portion without discontinuity with the contiguous portions having an external radius respectively equal to d and b; said parameters a, b, d, having been selected according to the optical characteristics of the lens to be obtained, taking into account the formulae: focal length f=ab/(a+b), aperture=2d, linear modification X=b/a (or X=a/b, according to the position of the image with respect to the source).
According to the invention, the parameter a, which gives the distance of the source or of the image from the center of the lens, may tend towards the infinite (a.fwdarw..infin.), the lens resulting in such a case is divided into three concentric zones, having respectively radius b, c and d.
Still according to the invention, the geodesic lens thus obtained may be employed in an optical processor of unidimensional signals, including:
an optical waveguide formed by a thin film of a material transparent to the laser radiation adopted and supported by a substrate made of a material having a refraction index inferior to that of the thin film; PA1 an optical system, manufactured on said substrate, formed by two geodesic lenses, the first of which having parameters a,b,c,d and the second one having parameters a',b',c',d', in such a way that the distance between the centers of the two lenses be equal or greater than the sum of the radius c of the first lens and of the radius a' of the second one. PA1 a modulator situated between the two lenses at a distance a' from the center of the second lens to insert the input signal along a line located perpendicularly to the axis which unites the centers of the two lenses. PA1 a filter located on a line parallel to the input line, at a distance a from the center of the first lens, and PA1 detecting means located on a circle having a radius equal to the focal length f of the second lens and having its center in a point situated on the line passing through the centers of the two lenses, at a distance a'-f from the center of said second lens.